This report describes numerical modeling work carried out on high Mach number flows. Three main technical areas were addressed: seamless transition of implicit large eddy simulation to direct numerical simulation, the development of secondary motion in corner flows, and large-scale unsteadiness of separated shock-wave/boundary-layer interactions. High-order numerical simulations of a Mach 2.3 turbulent equilibrium boundary-layer flow were performed with increasing resolution until all fluid scales in the domain were fully resolved. It was found that the high-fidelity implicit large-eddy simulations converged seamlessly to direct numerical simulation and the turbulent statistics were found to be essentially independent of the domain width for values greater than twice the maximum boundary layer thickness. Numerical simulations of turbulent equilibrium boundary layer flow in the presence of a second wall yielded the development of secondary motion, which significantly increased the three-dimensionality of the subsequent shock boundary-layer interaction in the system. Inclusion of both sidewalls was required to accurately predict the separation location. Introduction of the quadratic relationship into Reynolds-averaged Navier-Stokes models did generate secondary motion for compressible corner flows. However, the improved low-fidelity results did not fully match the high-fidelity implicit large eddy simulations. These results emphasize the need for and use of higher fidelity methods to reduce uncertainty and risk.